NCERT Class 7 Mathematics

214 MATHEMATICS

Consider the obtuse-angled triangle ABC of base 6 cm (Fig 11.16).

Its height AD which is perpendicular from the vertex A is outside the

triangle.

Can you find the area of the triangle?

EXAMPLE 6 One of the sides and the corresponding height of a

parallelogram are 4 cm and 3 cm respectively. Find the

area of the parallelogram (Fig 11.17).

SOLUTION Given that length of base (b) = 4 cm, height (h) = 3 cm

Area of the parallelogram =b × h

= 4 cm × 3 cm = 12 cm^2

EXAMPLE 7 Find the height ‘x’ if the area of the

parallelogram is 24 cm^2 and the base is

4 cm.

SOLUTION Area of parallelogram = b × h

Therefore, 24 = 4 × x(Fig 11.18)

or

24

4 =x or x= 6 cm

So, the height of the parallelogram is 6 cm.

EXAMPLE 8 The two sides of the parallelogram ABCD are 6 cm and 4 cm. The height

corresponding to the base CD is 3 cm (Fig 11.19). Find the

(i) area of the parallelogram. (ii) the height corresponding to the base AD.

SOLUTION

(i) Area of parallelogram =b × h

= 6 cm × 3 cm = 18 cm^2

(ii) base (b) = 4 cm, height = x (say),

Area = 18 cm^2

Area of parallelogram =b × x

18 = 4 × x

18

4 =x

Therefore, x= 4.5 cm

Thus, the height corresponding to base AD is 4.5 cm.

A

D C

4cm

B 6cm

Fig 11.16

Fig 11.17

Fig 11.18

A B

D C

x

4 cm

6 cm

3 cm

Fig 11.19